Your multimeter is almost certainly calibrated for a sine wave RMS reading. With other waveforms, especially pulses it will give a false reading.
The peak voltage is from the collapse of the current as the pulse ends and depends largely on how sharp the pulse edges are and how long the pulse lasts.
Those little pulses are almost certainly resonant effects, they indicate oscillation as some of the energy is re-absorbed and released again from the capacitor and driving circuit.
Brian.